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Number Theory and Symmetry

According to Carl Friedrich Gauss (1777–1855), mathematics is the queen of the sciences—and number theory is the queen of mathematics. Numbers (integers, algebraic integers, transcendental numbers, p-adic numbers) and symmetries are investigated in the nine refereed papers of this MDPI issue. This b...

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Formáid: Online
Teanga:Béarla
Foilsithe / Cruthaithe: MDPI - Multidisciplinary Digital Publishing Institute 2021
Ábhair:
quantum computation
IC-POVMs
knot theory
three-manifolds
branch coverings
Dehn surgeries
zeta function
Pólya-Hilbert conjecture
Riemann interferometer
prime numbers
Prime Number Theorem (P.N.T.)
modified Sieve procedure
binary periodical sequences
prime number function
prime characteristic function
limited intervals
logarithmic integral estimations
twin prime numbers
free probability
p-adic number fields ℚp
Banach ∗-probability spaces
C*-algebras
semicircular elements
the semicircular law
asymptotic semicircular laws
Kaprekar constants
Kaprekar transformation
fixed points for recursive functions
Baker’s theorem
Gel’fond–Schneider theorem
algebraic number
transcendental number
standard model of elementary particles
4-manifold topology
particles as 3-Braids
branched coverings
knots and links
charge as Hirzebruch defect
umbral moonshine
number of generations
the pe-Pascal’s triangle
Lucas’ result on the Pascal’s triangle
congruences of binomial expansions
primality test
Miller–Rabin primality test
strong pseudoprimes
primality witnesses
thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general
thema EDItEUR::P Mathematics and Science
Rochtain ar líne:ONIX_20210501_9783039366866_695
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Achoimre:According to Carl Friedrich Gauss (1777–1855), mathematics is the queen of the sciences—and number theory is the queen of mathematics. Numbers (integers, algebraic integers, transcendental numbers, p-adic numbers) and symmetries are investigated in the nine refereed papers of this MDPI issue. This book shows how symmetry pervades number theory. In particular, it highlights connections between symmetry and number theory, quantum computing and elementary particles (thanks to 3-manifolds), and other branches of mathematics (such as probability spaces) and revisits standard subjects (such as the Sieve procedure, primality tests, and Pascal’s triangle). The book should be of interest to all mathematicians, and physicists.

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